One of the founders of a major modern branch of complex analysis, Lipman Bers made fundamental contributions to the modern theory of Kleinian groups and moduli of Riemann surfaces. This volume is a collection of Bers' papers in complex analysis. Included are seminal papers in the field and articles by the editors and other colleagues discussing Bers' achievements and influence on the mathematical developments of the second half of the 20th century. Lists of his students, his publications, and reprints of hard-to-find papers are included.

Readership

Graduate students, research mathematicians and physicists working in complex analysis.

Reviews

"In bringing out this fine two-volume set, the editors have made a valuable contribution to the further development of complex analysis."

-- Mathematical Reviews

"The two volumes document the historical development and progress in research on the subjects made by one of its outstanding figures during almost half a century, with intimate connections to the work of others, including Ahlfors, I.N. Vekua, and the many students of Bers."

-- Zentralblatt MATH

Table of Contents

Part 1. Research Papers

On bounded analytic functions of two complex variables in certain domains with distinguished boundary surface

On rings of analytic functions

Singularities of minimal surfaces

Isolated singularities of minimal surfaces

Abelian minimal surfaces

Boundary value problems for minimal surfaces with singularities at infinity

Univalent solutions of linear elliptic systems

On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications

On linear and non-linear elliptic boundary values in the plane

Local behavior of solutions of general linear elliptic equations

An outline of the theory of pseudoanalytic functions

Formal powers and power series

On a theorem of Mori and the definition of quasiconformality

Simultaneous uniformization

Spaces of Riemann surfaces as bounded domains

Riemann's mapping theorem for variable metrics

Uniformization and moduli

Completeness theorems for Poincaré series in one variable

Quasiconformal mappings and Teichmüller's theorem

Spaces of Riemann surfaces

Holomorphic differentials as functions of moduli

Uniformization by Beltrami equations

The equivalence of two definitions of quasiconformal mappings

Holomorphic convexity of Teichmüller spaces

An approximation theorem

Automorphic forms and Poincaré series for infinitely generated Fuchsian groups

Automorphic forms and general Teichmüller spaces

A non-standard integral equation with applications to quasiconformal mappings